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<table width="100%"><tr><td>prof.dev(gamlss)</td><td align="right">R Documentation</td></tr></table><object type="application/x-oleobject" classid="clsid:1e2a7bd0-dab9-11d0-b93a-00c04fc99f9e">
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<h2>Plotting the Profile Deviance for one of the Parameters in a GAMLSS model</h2>


<h3>Description</h3>

<p>
This functions plots the profile deviance of one of the (four) parameters in a GAMLSS model. It can be used if one 
of the parameters <code>mu</code>, <code>sigma</code>, <code>nu</code> or <code>tau</code> is a constant (not a function of explanatory variables) to obtain 
a profile confidence intervals.
</p>


<h3>Usage</h3>

<pre>
prof.dev(object, which = NULL, min = NULL, max = NULL, step = NULL, 
          startlastfit = TRUE, type = "o", plot = TRUE, perc = 95, 
          ...)
</pre>


<h3>Arguments</h3>

<table summary="R argblock">
<tr valign="top"><td><code>object</code></td>
<td>
A fitted GAMLSS model</td></tr>
<tr valign="top"><td><code>which</code></td>
<td>
which parameter to  get the profile deviance e.g. <code>which="tau"</code></td></tr>
<tr valign="top"><td><code>min</code></td>
<td>
the minimum value for the parameter e.g. <code>min=1</code></td></tr>
<tr valign="top"><td><code>max</code></td>
<td>
the maximum value for the parameter e.g.  <code>max=20</code></td></tr>
<tr valign="top"><td><code>step</code></td>
<td>
how often to evaluate the global deviance (defines the step length of the grid for the parameter) e.g. <code>step=1</code> </td></tr>
<tr valign="top"><td><code>startlastfit</code></td>
<td>
whether to start fitting from the last fit or not, default value is <code>startlastfit=TRUE</code>  </td></tr>
<tr valign="top"><td><code>type</code></td>
<td>
what type of plot required. This is the same as in <code>type</code> for <code>plot</code>, default value is <code>type="o"</code>, that is, both line and points </td></tr>
<tr valign="top"><td><code>plot</code></td>
<td>
whether to plot, <code>plot=TRUE</code> or save the results, <code>plot=FALSE</code>  </td></tr>
<tr valign="top"><td><code>perc</code></td>
<td>
what % confidence interval is required </td></tr>
<tr valign="top"><td><code>...</code></td>
<td>
for extra arguments</td></tr>
</table>

<h3>Details</h3>

<p>
This function can be use to provide likelihood based confidence intervals for a parameter for which a constant model (i.e. no explanatory model) is fitted and
consequently for checking the adequacy of a particular values of the parameter. This can be used to check the adequacy of one distribution (e.g. Box-Cox Cole and Green) 
nested within another (e.g. Box-Cox power exponential). For example one can test whether a Box-Cox Cole and Green (Box-Cox-normal) distribution 
or a Box-Cox power exponential is appropriate by plotting the profile of the parameter <code>tau</code>. 
A profile deviance showing support for  <code>tau=2</code> indicates adequacy of the Box-Cox Cole and Green (i.e. Box-Cox normal) distribution.
</p>


<h3>Value</h3>

<p>
A plot of profile global deviance</p>

<h3>Warning</h3>

<p>
A dense grid (i.e. small step) evaluation of the global deviance can take a long time, so start with a sparse grid (i.e. large step) 
and decrease  gradually the step length for more accuracy.
</p>


<h3>Author(s)</h3>

<p>
Calliope Akantziliotou, Mikis Stasinopoulos <a href="mailto:d.stasinopoulos@londonmet.ac.uk">d.stasinopoulos@londonmet.ac.uk</a> and Bob Rigby <a href="mailto:r.rigby@londonmet.ac.uk">r.rigby@londonmet.ac.uk</a>
</p>


<h3>References</h3>

<p>
Rigby, R. A. and  Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), 
<EM>Appl. Statist.</EM>, <B>54</B>, part 3, pp 507-554.
</p>
<p>
Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R.
Accompanying documentation in the current GAMLSS  help files, (see also  <a href="http://www.gamlss.com/">http://www.gamlss.com/</a>).  
</p>
<p>
Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R.
<EM>Journal of Statistical Software</EM>, Vol. <B>23</B>, Issue 7, Dec 2007, <a href="http://www.jstatsoft.org/v23/i07">http://www.jstatsoft.org/v23/i07</a>.
</p>


<h3>See Also</h3>

<p>
<code><a href="gamlss.html">gamlss</a></code>,  <code><a href="prof.term.html">prof.term</a></code>
</p>


<h3>Examples</h3>

<pre>
data(abdom)
h&lt;-gamlss(y~cs(x,df=3), sigma.formula=~cs(x,1), family=BCT, data=abdom) 
prof.dev(h,"nu",min=-2.000,max=2,step=0.25,type="l")
rm(h)
</pre>



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